If you see a threat of harm (including self-harm):

Many threats are empty, but Wikipedians do not have the training to make such evaluations.
If you are in immediate danger, call your local emergency services.

Immediately email emergencywikimedia.org with details of the threat.

If you have a registered account and have email enabled, you can also use Special:EmailUser/Emergency to contact the Foundation.
This address is only for true emergencies and is monitored around the clock. If you have an issue that is not an emergency, please see Wikipedia:Contact us for a more appropriate venue.
Include the name of the page where the threat was made, or a diff.
Avoid emailing other addresses or telephoning the Wikimedia Foundation office, as it creates confusion.
Staff will typically acknowledge your email immediately.
Staff will take appropriate action, such as tracing locations and contacting authorities.

In addition to emailing the Wikimedia Foundation as above, notify Wikipedia administrators privately.

Even an administrator discovering a threat should notify other administrators.
Use email, IRC, or other low-visibility methods. Avoid high-traffic noticeboards when reporting.
If in doubt, join #wikipedia-en-revdel ^connect or failing that, in true emergencies there is almost always a steward on #wikimedia-stewards ^connect. If you don't have an IRC client, click the green ^connect button to launch web-based IRC.
Also request oversight, as such posts often contain personal information requiring suppression.

Advice for administrators

Threats of violence against others should be met with blocking, generally including removal of talk page access, and possibly blocking email. Such threats should be removed from any relevant pages. Consider also deleting the problematic revision from public view.
Threats of suicide or self-harm require discretion on the questions of blocking or removal of posts.
If in doubt, email the office at emergencywikimedia.org.

Notes

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